An information-theoretic analysis of resampling in Sequential Monte Carlo
Author(s)Huggins, Jonathan H. (Jonathan Hunter)
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Joshua B. Tenenbaum.
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Sequential Monte Carlo (SMC) methods form a popular class of Bayesian inference algorithms. While originally applied primarily to state-space models, SMC is increasingly being used as a general-purpose Bayesian inference tool. Traditional analyses of SMC algorithms focus on their usage for approximating expectations with respect to the posterior of a Bayesian model. However, these algorithms can also be used to obtain approximate samples from the posterior distribution of interest. We investigate the asymptotic and non-asymptotic properties of SMC from this sampling viewpoint. Let P be a distribution of interest, such as a Bayesian posterior, and let P be a random estimator of P generated by an SMC algorithm. We study ... i.e., the law of a sample drawn from P, as the number of particles tends to infinity. We give convergence rates of the Kullback-Leibler divergence KL ... as well as necessary and sufficient conditions for the resampled version of P to asymptotically dominate the non-resampled version from this KL divergence perspective. Versions of these results are given for both the full joint and the filtering settings. In the filtering case we also provide time-uniform bounds under a natural mixing condition. Our results open up the possibility of extending recent analyses of adaptive SMC algorithms for expectation approximation to the sampling setting.
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.29Cataloged from student submitted PDF version of thesis.Includes bibliographical references (pages 56-57).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology
Electrical Engineering and Computer Science.